Set is Subset of Pre-Image of Image
Set is Subset of Pre-Image of Image
For \(f : X \to Y\) and \(A \subseteq X\)
\[ A \subseteq f^{-1}(f(A))\]
and in particular
\[ A = f^{-1}(f(A)) \quad \forall A \subseteq X \iff f \ \text{is injective}\]